Workshop on Modern Trends in Mathematical Crystallography

In recent years, the area of mathematical crystallography has grown beyond the traditional study of the fundamental properties of symmetry and periodicity of crystals. This expanded horizon was the subject of the workshop 'Modern Trends in Mathematical Crystallography' (MathCryst Manila 2017), held in the Ateneo de Manila University in Quezon City, Philippines, from 20 to 24 May 2017, which introduced participants to current topics and new directions in mathematical crystallography and its applications. New trends in group and graph theory, as well as topological aspects of mathematical crystallography, were focal points. In this second mathematical crystallography workshop held in the country (the first one dates back to November 2011), there were eight invited speakers, experts in their respective fields, who gave talks on topics ranging from discrete models of crystals, periodic to aperiodic, to highly ordered structures. The expected outcomes of the workshop for the participants included exposure to research opportunities in mathematical crystallography, heightened awareness of the relevance of crystallography in their research, and starting or continuing collaborations between researchers.

The workshop began with a brief opening programme, where Ateneo de Manila University officials welcomed the speakers and participants. Ma. Louise Antonette De Las Peñas, Local Organizing Committee Chair, gave the participants an overview of how mathematical crystallography started in the Philippines. The workshop proper followed, starting with a lecture from Jean-Guillaume Eon (Federal University, Rio de Janeiro, Brazil) about the Topology of Crystal Structures: Applications of Graph Theory and followed by a lecture on Domain Structures by Massimo Nespolo (University of Lorraine, France). On the second day of the workshop, Egon Schulte (Northeastern University, Boston, MA, USA) and Stephen Hyde (Australian National University, Canberra, Australia) lectured, respectively, on Polyhedra, Complexes, Nets, and Symmetry and Two Dimensional Crystallography via Orbifolds. On the third day, participants explored the Bilbao Crystallographic Server: Mathematical Crystallography Tools in Material Studies through a workshop conducted by Mois Aroyo (University of the Basque Country, Bilbao, Spain). Dirk Frettloeh (Bielefeld University, Germany) gave two lectures, Quasicrystals and Symmetry on the third day, and Average Lattices for Quasicrystals on the fourth day. Shigeki Akiyama (Tsukuba University, Japan) gave a lecture on Beta Expansions and Self-Affine Tilings, also on the fourth day. Finally, on the fifth day, Marjorie Senechal (Smith College, Northhampton, MA, USA) gave a lecture on Icosahedral Snowflakes.

Local Organizing Committee with speakers.

MathCryst Manila 2017 had 65 participants, including 14 members of the Local Organizing Committee. 19 participants presented posters during a poster session on the third day of the workshop, showcasing their research related to mathematical crystallography. The organizers set up tea and lunch breaks to give time for socialization and relaxation, as well as opportunities for participants to have discussions among themselves and with the speakers about mathematics and crystallography. Very notable was the fact that the students were very eager and excited to interact with the speakers and ask questions. For most of the students, this was their first chance to attend an international workshop and to learn about mathematical crystallography.

During the final programme held on the last day of the workshop, gifts of appreciation were given to the speakers, and certificates of attendance distributed to the participants by the Local Organizing Committee. A couple of participants were asked to speak about their experiences during the workshop. Gwendolyn Tadeo, a graduate student of the Ateneo de Manila University, spoke on behalf of the other students in attendance, and summarized her experience as follows: 'This has been a venue for me, for us, to learn more about the area of crystallography, how really beautiful it is, and opens the possibility of exploring more of its beauty with the help of mathematics. With all the talks that we had from our speakers, I would use the words overwhelming and profound to describe the experience of being able to listen, comprehend and digest everything that has transpired the past five days. I'll say after this workshop, I'm already trying to consider a research area related to tilings or crystallography. It was such a great experience to have attended this workshop, and this experience has made me realize again and again, that as long as there are questions to be asked, and answers to be found, mathematicians never stop'.

IUCr Young Scientist Awardees.

MathCryst Manila 2017 would not have been a success if it were not for the speakers' generosity and commitment, the hardworking members of the Local Organizing Committee from the Department of Mathematics, Ateneo de Manila University, and the help and sponsorship of the South East Asian Mathematical Society (SEAMS), the Mathematical Society of the Philippines (MSP), and the Ateneo de Manila University. Special mention goes to the IUCr and its Commission on Mathematical and Theoretical Crystallography for the organizational support, travel support for visiting professors and young scientists to attend the workshop, and above all for providing the opportunity to have a second mathematical crystallography workshop in the Philippines.

We hope that with this workshop, more fruitful collaborations will spring forward, and that current research partnerships will be further strengthened. We certainly are looking forward to a third mathematical crystallography workshop in the Philippines in the near future!